1. Field of the Invention
The present invention relates to the petroleum industry, and more particularly to petroleum reservoir characterization by construction of a representation of the reservoir referred to as reservoir model. In particular, the invention relates to a method of updating a reservoir model after acquiring new measurements from the petroleum reservoir.
2. Description of the Prior Art
Optimization and development of petroleum reservoirs are based on the most accurate possible description of the structure, the petrophysical properties, the fluid properties, etc., of the reservoirs. A tool accounting for these aspects in an approximate way is a reservoir model. The model is of the subsoil which is representative of both its structure and its behavior. Generally, this type of model is represented in a computer and is referred to as a numerical model.
Reservoir models are well known and widely used in the petroleum industry to determine many technical parameters relative to prospecting, study or development of a reservoir such as, for example, a hydrocarbon reservoir. In fact, a reservoir model is representative of the structure of the reservoir and of the behavior thereof. It is thus, for example, possible to determine which zones are the most likely to contain hydrocarbons, the zones in which it can be interesting/necessary to drill an injection well in order to enhance hydrocarbon recovery, the type of tools to use, the properties of the fluids used and recovered, etc. These interpretations of reservoir models in terms of “technical development parameters” are well known, even though new methods are regularly developed. It is thus crucial, in the petroleum industry, to construct a model as precisely as possible. Integration of all the available data is therefore essential.
The purpose of a reservoir model is to best account for all the information relative to a reservoir. A reservoir model is representative when a reservoir simulation provides historical data estimations that are very close to the observed data. What is referred to as historical data are the production data obtained from measurements in wells in response to the reservoir production (oil production, water production of one or more wells, gas/oil ratio (GOR), production water proportion (water cut)), and/or repetitive seismic data (4D seismic impedances in one or more regions, etc.). A reservoir simulation is a technique allowing simulation of fluid flows within a reservoir by a software based flow simulator.
History matching modifies the parameters of a reservoir model, such as permeabilities, porosities or well skins (representing damages around the well), fault connections, etc., in order to minimize differences between the simulated and measured historical data. The parameters can be linked with geographic regions, such as permeabilities or porosities around one or more wells.
A reservoir model has a grid with N dimensions (N>0 and generally two or three) in which each cell is assigned the value of a property characteristic of the zone being studied. It can be, for example, the porosity or the permeability distributed in a reservoir. FIG. 1 shows a facies map of a petroleum reservoir, making up a two-dimensional reservoir model. The grid pattern represents the cells. The grey cells represent a reservoir facies zone and the white cells represent a non-reservoir facies zone.
The value of a property characteristic of the zone being studied is referred to as a regionalized variable which is a continuous variable, spatially distributed, and representative of a physical phenomenon. From a mathematical point of view, the regionalized variable is simply a function z(u) taking a value at each point u (the cell of the grid) of a field of study D (the grid representative of the reservoir). However, the variation of the regionalized variable in this space is too irregular to be formalized by a mathematical equation. In fact, the regionalized variable represented by z(u) has both a global aspect relative to the spatial structure of the phenomenon under study and a random local aspect.
This random local aspect can be modelled by a random variable (VA). A random variable is a variable that can take on a number of realizations z according to a probability law. Continuous variables such as seismic attributes (acoustic impedance) or petrophysical properties (saturation, porosity, permeability) can be modelled by VAs. Therefore, at point u, the regionalized variable z(u) can be considered to be the realization of a random variable Z.
However, to properly represent the spatial variability of the regionalized variable, it must be possible to take into account the double aspect, both random and structured. One possible approach, of probabilistic type, involves the notion of random function. A random function (FA) is a set of random variables (VA) defined in a field of study D (the grid representative of the reservoir), that is {Z(u), u*D}, also denoted by Z(u). Thus, any group of sampled values {z(u1), . . . , z(un)} can be considered to be a particular realization of random function Z(u)={Z(u1), . . . , Z(un)}. Random function Z(u) allows accounting for both the locally random aspect (at u*, the regionalized variable z(u*) being a random variable) and the structured aspect (via the spatial probability law associated with random function Z(u)).
The realizations of a random function provide stochastic reservoir models. From such models, it is possible to appreciate the way the underground zone works under study. For example, simulation of the flows in a porous medium represented by numerical stochastic models allows, among other things, prediction of the reservoir production and optimizing its development by testing various scenarios.
Construction of a stochastic reservoir model can be described as follows:
First, static data are measured in the field (logging, measurements on samples taken in wells, seismic surveys, . . . ) and, dynamic data are measured (production data, well tests, breakthrough time, . . . ), whose distinctive feature is that they vary over time as a function of fluid flows in the reservoir,
then, from the static data, a random function characterized by its covariance function (or similarly by its variogram), its variance and its mean is defined,
a set of random numbers drawn independently of one another is defined: which can be, for example, a Gaussian white noise or uniform numbers. Thus, an independent random number per cell and per realization is obtained,
finally, from a selected geostatistical simulator and from the set of random numbers, a random draw in the random function is performed, giving access to a (continuous or discrete) realization representing a possible image of the reservoir. Conventionally, the random draw is performed in a hierarchical context. First, the reservoir is randomly populated by a realization of the random function associated with the facies, conditionally to the facies measurements taken punctually. Then, the porosity is generated randomly on each facies which is conditionally to the porosity data obtained on the facies considered. The horizontal permeability is then simulated according to its associated random function, conditionally to the facies and to the porosities drawn before, and to the permeability measurements taken in the field. Finally, the reservoir is populated by a random realization of the vertical permeability, conditionally to all the previous simulations and to the permeability data obtained punctually.
At this stage, the dynamic data have not been considered. They are integrated in the reservoir models via an optimization or a calibration. An objective function measuring the difference between the dynamic data measured in the field and the corresponding responses simulated for the model considered is defined. The goal of the optimization procedure is to modify little by little this model so as to reduce the objective function. Parametrization techniques allow these modifications to be provided while preserving coherence with respect to the static data.
In the end, the modified models are coherent with respect to the static data and the dynamic data. It must be possible to update these models completely so that when new data are available the model has to be modified to account for the new data. The calibration and parametrization techniques are improving continuously. Consequently, reservoir engineers frequently need to go back over reservoir models elaborated and calibrated in the past. The goal is to refine these models and to update them with the data acquired since the time when the model had been initially elaborated.
However, an essential difficulty still remains when going back over numerical models elaborated in the past. In fact, to apply a method allowing refinement calibration of an existing realization, the number of random numbers which, when given to the geostatistical simulator, provides the numerical model (the realization) in question has to be known. Now, in general, this information no longer exists. Similarly, the variogram (or covariance) model characterizing the spatial variability in the underground zone of the represented attribute and necessary to characterize the random function is no longer known. The latter point is less important insofar as a study of the existing numerical model can allow to find this variogram again.
French Patent 2,869,421 discloses a method for reconstruction of numerical stochastic models, that is, for a previously determined random function, to identify a set of random numbers which, given as input data to a geostatistical simulator, provides a realization similar to the numerical model being considered. However, this technique applies to continuous variables representative, for example, of the porosity, that is to the case of a reservoir comprising a single facies.